THE PHYSICAL UNIVERSE. PART 5.

THE PHYSICAL UNIVERSE PART V.

CHAPTER V.

A BLACK-HOLE.

The idea that there exists in nature "dark stars" with such a strong gravitational force that not even light can escape from them has been around for a long time. John Michell (1724-1793) presented such an idea in 1783 to the Royal Society and Pierre Simon Laplace (1749-1827)independently published the same ideas in 1796. The idea was almost forgotten in the 19Th century but became popular after Albert Einstein’s general theory of relativity. Black Holes are thought to be formed as a result of the explosions of massive stars in supernova. Calculations have shown that compact supernova remnant with more mass than three times the mass of the sun would collapse into a black hole. It is thought today that there exists a "super massive black hole" at the heart of every galaxy.

There is not much known about the black hole but it is speculated that the escape velocity is equal to that of the speed of light. This would mean that mass and energy of the universe can fall in or be absorbed by a black hole, but nothing, no mass, no energy, not even light, can escape from it. The boundary of a black hole is known as the "event horizon" beyond which nothing can be observed from the outside. It was Karl Scharzschild (1873-1916) who discovered the solution of Einstein’s general relativity equation that described a black hole and worked out the formula of its critical radius. This is known as the Schwarzschild radius:

R = ( 2 G M ) / c^2

where (R) is the radius of a black hole, (G) is the gravitational constant, (M) is its mass and (c) is the velocity of light.

Theoretically, a black hole can be characterised by its mass, angular momentum and by its electrical charge. Apart from these three properties theorists are not certain but they speculate that there exists various kinds of black holes. There are the uncharged, non-rotating black hole described by the Schwarzschild solution; a charged, non-rotating black hole described by the Reissner-Nordstrom solution; an uncharged but rotating black hole described by the Ker solution; and a rotating, charged black hole described by the Ker-Newman solution.

Cosmologists trying to follow the general relativity theory, speculate that the ultimate fate of matter inside the event horizon, is its consumption in a singularity. This is a point where its density is infinite, its space is one-dimensional and where the laws of physics as far as we know, break down. The singularity is a point of infinite density that is speculated to be the end of matter according to the mathematical equation of Einstein’s general relativity theory. It is also speculated that the mirror image of such a singularity is the uniform expansion of the universe as described by the big bang theory. This implies that it was a singularity from which the universe was born.

There have been attempts to discover a mathematical solution that would unite gravity and quantum theory. One of these attempts was made by Roger Penrose (1931-- ) who proved that any mass falling into a non-rotating black hole was crushed into a singularity. However, the big problem of the singularity is that it does not account for the quantum theory but only is a solution to a question that arises from gravity and the general relativity theory.

What is here proposed is to examine the black hole from both the relativity theory and the quantum theory as it is explained above. If one takes a black hole consisting only of quanta particles it must have virtual mass according to the formula:

m^0 = (f h) / c^2

where (m^0) is the quantity of virtual mass, (f) is the frequency of the quanta particles, (h) is the Planck constant, and (c) is the velocity of light. Since the black hole consists of G E virtual mass it must also have energy which is of two kinds; kinetic and gravitational energies. The formula for its kinetic energy is:

K E = ( m^0 c^2 ) / 2

and its formula for its gravitational energy is:

G E = ( G ( m^0 )^2) / R

where (G) is the gravitational constant and (R) is the Schwarzschild radius of the black hole. From the energy formula is possible to work out the radius of the black hole:

E = K E + G E

m^0 c^2 = (( m^0 c^2 ) / 2 ) + ( G ( m^0 )^2) / R

(( m^0 c^2 ) / 2 ) = ( G ( m^0 )^2 ) / R

R = ( 2 G m^0 ) / c^2

However, since the virtual mass is:

M^0 = ( f h ) / c^2

the radius of the event horizon of a black hole is:

R = ( 2 G f h ) / c^4

In such a black hole consisting only of pure or radiant energy its time dimension is zero because all the quanta particles move at the velocity of light. In other words, it exists in the fifth dimension or frame reference. There are no other dimension within it because it contains no massive objects that move with a speed lesser than the speed of light. The black hole also has a temperature and density depending on the amount of quanta energy which will decrease as its energy or virtual mass increases. The decrease of temperature and density is due to the increase of the energy or virtual mass because density is measured by the mass divided by its volume which depends on its radius:

D = M / V

The volume of a sphere increases by the cube root of its increase of the radius:

V = ( 4 pi R ^3 ) / 3

The radius of a black hole increases directly by the increase of its mass:

R = ( 2 G M ) / c^2

and thus the volume of the sphere of a black hole increases by the cube of its increase of its mass, and its density decreases by the square of its mass. The fact that the density of a black hole decreases much faster than its increase of its mass or energy is an important phenomenon that will be shown later when discussing quantum fluctuation and the formation of mass particles.

Since a black hole consisting of pure energy, exists in the fifth dimension or frame reference, the Newtonian laws of movement apply because all the quanta particles move at the same velocity relative to one another and the time dimension does not apply because they all move at the speed of light.

Another very important phenomenon of a black hole consisting of pure energy is that there is no place for a singularity. This is so because all the quanta particles or virtual mass have momentum, kinetic and gravitational energies that can not be destroyed, but are conserved due to the law of conservation of energy.

The quanta particles within a pure energy black hole are not drawn to its centre because here there exists an equilibrium of its gravitational and kinetic force. As it was shown earlier in this work, quanta particles have two equal and opposite forces, kinetic and gravitational. It could be argued that the gravitational force within a black hole is most active at its boundary within its event horizon because it prevents the quanta particles from escaping.

This is not a strange phenomenon because even in our ordinary experience of a massive object, its centre of gravity may lie within or without the object. It is at the centre of gravity that all the forces of gravity of the object full equally in all direction so that there is an equilibrium at its centre and the object is at rest or has equilibrium. In a black hole the greatest pull of gravity is not at its centre but at its boundary while at its centre there is an equilibrium. The quanta particles cannot be collected at its centre because they cannot loose any energy and momentum which are conserved. There exists an equilibrium within a pure black hole because the gravitational forces are equally opposed by the kinetic forces. Both these forces are potential and conserved in the kinetic and gravitational energies of the quanta particles.

If a singularity cannot exist at the centre of a pure energy black hole, than no singularity can exist in the universe. This is so because matter reduced to its most basic form is pure energy and this is according to Einstein’s relativity theory which holds that mass can be reduced to pure energy and energy can be transformed into mass.

A singularity is not possible because it does not account for the momentum of quanta particles which does exists according to Einstein’s photo electron effect. Both the gravity and momentum of quanta particles cannot be lost because quanta particles cannot loose any energy; they are the most basic quantity of energy according to Planck’s theory. The theory of the singularity only deals with gravity and does not account for the momentum of quanta particles.

While a black hole cannot loose any energy, it can, however, gain energy from the outside. Let us presume that a pure energy black hole only gains pure energy. As it gains energy, it will gain virtual mass and consequently its radius will increase and its density will decrease. However, it will retain its equilibrium at its centre while the strength of its gravitational force and thus its pressure and temperature remains the same at its event horizon, preventing any escape of quanta particles.

It could be speculated that in nature there exists no greater force of gravity, pressure and temperature than at the event horizon of a black hole because nothing can move faster than the speed of light or quanta particles. If this speculation is correct that the greatest region of density and temperature is at the event horizon of a black hole, it could also be speculated that it is the optimum place for the occurrence of quantum fluctuation as Stephen Hawking has proposed.

Quantum fluctuation is due to the Heisenberg uncertainty principle operating in nature where matter and anti-matter is formed. Stephen Hawking speculated that quantum fluctuation forming matter and anti-matter occurs just outside the event horizon of a black hole. He further speculated that this pair of matter and anti- matter could exist for a very brief moment of time before dissolving again. But in this brief moment of time it could happen that one part of the paired particle matter fell into the black hole, the other part gained energy from the black hole and could thus escape into the universe. By this means, he said, a black hole could loose energy and could possibly even explode forming a white hole. It was even speculated that this could have been the big bang or the creation of the universe.

Quantum fluctuation could be interpreted as the mechanism by which the universe transforms quanta particles or virtual mass into massive objects like sub-atomic particles. This process would not violate any principles. The pair of matter and anti-matter would not just pop out of nothing but are formed from the quanta particles which posses virtual mass and both gravitation and momentum.